Understanding Stencils in Finite Difference Methods

[alecrimi]

Hi
Sorry for the stupid question, but what is exactly a "stencil" in finite difference methods ?
Is the results of the expansion points ?
Cheers
Alex

 

[hunt_mat]

This is also called a computational molecule in some texts, it basically is the recurrence relation that you use to calculate the next point in your calculation, so for example a stencil for the Euler method for the ODE $\frac{du}{dx}=f(x,u)$ would be:
$$u_{n+1}=u_{n}+hf(x_{n},u_{n})$$
For PDEs it would be something more complicated. I hope you get the general idea.